On the coupling between the plant and controller optimization problems

This paper examines the plant and controller optimization problems. One can solve these problems sequentially, iteratively, using a nested (or bi-level) strategy, or simultaneously. Unlike the nested and simultaneous strategies, the sequential and iterative strategies fail to guarantee system-level optimality. This is because the plant and controller optimization problems are coupled. This coupling is introduced using a simple experiment. To prove it theoretically, the necessary conditions for combined plant and controller optimality are derived. These combined optimality conditions differ from the individual sets of necessary conditions for plant and controller optimality by a coupling term that reflects the plant design's influence on the plant dynamics and control input constraints.